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Lecture 1 - statistics numerical methods graphics etc...

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EGM3344 Introduction to Numerical Methods of Engineering Analysis
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Course Objectives To develop the ability to solve engineering problems numerically To evaluate numerical solution methods ( knowing the advantages and limitations of numerical methods) To design , implement , and test computer programs To learn the skills of writing MATLAB codes
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Chapter 1 Mathematical Modeling and Engineering Problem Solving
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Solving Engineering Problems Empirical observation and experiment certain aspects of empirical studies occur repeatedly such general behavior can be expressed as fundamental laws that essentially embody the cumulative wisdom of past experience Theoretical / Numerical formulation of fundamental laws Algebraic ODE PDE q y T x T dt x d m dt dv m F E ; ma F = + = = = = 2 2 2 2 2 2 ε σ
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Mathematical Models Modeling development of a mathematical representation of physical/biological/chemical/ economic/... system Problem Solving Tools : Analytic solutions,
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Unformatted text preview: statistics, numerical methods , graphics, etc. Mathematical Modeling The process of solving an engineering or physical problem. Bungee Jumper You are asked to predict the velocity of a bungee jumper as a function of time during the free-fall part of the jump Use the information to determine the length and required strength of the bungee cord for jumpers of different mass The same analysis can be applied to a falling parachutist or a rain drop, ballistic trajectories. The world's first electronic digital computer was developed by Army Ordnance to compute World War II ballistic firing tables . Newton’s Second Law (downward is assumed +ve) F = ma = F down- F up = mg - c d v 2 (gravity minus air resistance) Observations / Experiments (Where does mg come from? Where does -c d v 2 come from?) Bungee Jumper y, v, a mg v 2...
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